Summary: In this paper, we deal with some geometric properties of an \(\alpha\)-cosymplectic manifold. First, we give some classifications for an \(\alpha\)-cosymplectic manifold endowed with some special vector fields such as projective, concircular and torse-forming. Then, we study \(\alpha\)-cosymplectic manifold admitting \(\eta\)-Ricci solitons with projective, affine conformal vector fields. Finally, we obtain some characterizations for such a manifold to be Einstein, \(\eta\)-Einstein, cosymplectic.